Carnival CEO Gerry Cahill says the cruise line is making passengers aboard the disabled ship Triumph as comfortable as possible as it's being towed into Mobile, Ala., but acknowledged conditions on board the ship are "challenging."

Cahill said late Tuesday that the ship has running water and most of its 23 public restrooms and some of the guest cabin bathrooms are working.

He downplayed the possibility of an outbreak of disease from unsanitary conditions, saying the ship hasn't seen an abnormal number of people reporting to the infirmary as being ill.

"No one here from Carnival is happy about the conditions on board the ship," Cahill said at a news conference in Miami. "We obviously are very, very sorry about what is taking place."

The ship is expected to reach Mobile, Ala., on Thursday. Carnival has booked 1,500 hotel rooms in the area to accommodate passengers on Thursday night and has arranged for 20 charter flights to return them home on Friday, Cahill said.

Passengers on the 102,000-ton ship who have been able to reach relatives and news outlets have described overflowing toilets and a stench so bad that it was making some passengers sick.

"There's water and feces all over the floor," one of the passengers told her husband, Brian Nutt, in a call from the ship on Monday. "The whole ship stinks extremely badly."

Nutt said his wife described passengers throwing up from the stench. "You would think Carnival would have something in place to get these people off the ship," he said.

The ship was left adrift in the Gulf of Mexico on Sunday after a fire broke out in the engine room.

The U.S. Coast Guard, along with a team from the National Transportation Safety Board, announced Tuesday that it has opened an investigation into the cause of the fire. The NTSB said the Bahamas Maritime Agency will lead the investigation because the ship carries a Bahamian flag.

"We have investigators who are mariners as well," said NTSB spokesman Keith Holloway, and an expert in finding the cause of fires. "They have investigated other fires on cruise ships."

Although the blaze was contained, Carnival said, it knocked out the power that runs air conditioning, elevators and toilets in passenger areas and kitchen equipment used to prepare hot meals.

The vessel's freshwater system was knocked down until Monday, Carnival said, when toilets in some areas of the ship were working again. Enough power was restored to allow for some hot food at a buffet.

Still, conditions have remained difficult, with passengers relaying stories of long lines for meals and people sleeping on open decks.

Jay Herring, a former senior officer for Carnival Cruise Lines, said one of the biggest concerns crew members will have until the ship docks is the potential for disease outbreak, particularly norovirus, which causes vomiting and diarrhea.

"Housekeeping, others are probably working double shifts to keep the mess clean and wipe down and sanitize all the common areas," said Herring, who worked for Carnival from 2002 to 2004 and spent four months on the Triumph.

It emerged Tuesday that the ship had been listing about 4.5 degrees on Monday, which Carnival attributed to strong winds.

Carnival spokesman Vance Gulliksen said the list diminished to about 2 degrees Tuesday after tugboats began towing the vessel. The listing poses no safety risk, Carnival said.

The cruise line evaluated options and decided the safest alternative was to tow the ship back to port, Gulliksen said.

Because Carnival ships tend to sail full, there may have been no space to accommodate passengers on other ships, retired cruise line executive Art Sbarsky said.

"Given a choice, I'd rather be on a ship the size of Triumph than bobbing around in a (life boat)," Sbarsky said.

The Carnival Triumph has been under tow since late Monday, when the first of two tugboats arrived to pull the vessel to Mobile, Ala. It's scheduled to arrive Thursday afternoon.

The ship was 150 miles from the coast of Mexico when it lost power, and Carnival initially planned to tow it to the Mexican port of Progreso, but strong currents pushed the ship 90 miles north by the time tugs reached the vessel, making a tow to Alabama more logical.

As of Tuesday afternoon, the ship was about 250 miles south of Mobile, according to the U.S. Coast Guard.

None of the 3,143 passengers and 1,086 crew on board the Carnival Triumph was injured during the fire, and only one medical issue has since been reported.

On Monday, a passenger in need of dialysis was transferred to the Carnival Legend for transport to Cozumel, Mexico. Arriving Monday afternoon, the Legend also provided meals for passengers on the Triumph - and a chance for some passengers to communicate with home.

With much of the power on the Carnival Triumph down, passengers with cellphones have been able to call and text from the vessel only during brief periods when another Carnival ship with connectivity pulls alongside - a fact that has left some family members back at home frustrated.

"It's stressful," Danny Price of Oklahoma told Tulsa's KJRH-TV of not being able to talk to his wife and other relatives on the vessel. "I'd like to hear from her and know that she's all right and being taken care of."

Travel agent Monte Akers of CruiseOne in Houston said he hasn't heard from a family of six he had booked on the sailing, but he said he was impressed with how Carnival was handling the situation so far.

Carnival CEO Gerry Cahill apologized to passengers in a statement late Monday, saying, "We're terribly sorry for the inconvenience, discomfort, and frustration our guests are feeling.

"We know they expected a fantastic vacation, and clearly that is not what they received," he said.

Within hours of the fire, Carnival announced that passengers on the ship would get full refunds, and it later added a credit for a future cruise.

"Typically when these things happen, cruise lines will give vouchers for only a portion of the cruise," Akers said.

At the time of the fire, the Carnival Triumph was near the end of a four-night cruise to Mexico out of Galveston, Texas, which began on Thursday. The ship had been scheduled to return to Galveston early Monday.

The Carnival Triumph fire is just the latest in a string of serious incidents involving cruise ships.

The most serious was the capsizing of the Costa Concordia in January 2012 in Italy that left 32 passengers dead.